The story of the N.C.A.A. men’s basketball tournament is Florida Gulf Coast University, which on Sunday became the first No. 15 seed ever to reach the Round of 16, despite having become a full Division I member only last season. Just how unlikely was its accomplishment? Does the team have a chance of advancing much further? And what about the other teams in the Round of 16?

In fact, we have been updating our tournament odds after almost every game. The first week of the tournament has been consequential for teams beyond Florida Gulf Coast. Louisville, a modest front-runner to win the tournament before it began, has become a clearer one now. Florida and Syracuse have also seen their chances improve considerably. Other teams like Indiana, however, have actually seen their odds decline.

There are two major factors that account for the shift in the odds from game to game. One is that our system adjusts its estimate of each team’s strength based on its margin of victory in games so far. A team that wins but does so by an underwhelming margin against a subpar opponent, as Gonzaga did in its first game against Southern University, can be a good candidate to be upset later on (as Gonzaga was by Wichita State). A team that wins in dominating fashion may be adjusting well to the contours of tournament play, by contrast.

The other major factor is what has happened to the opponents that a team is most likely to face: have upsets helped clear out its draw, or instead, is a team running headlong into a series of tough opponents? (Injuries, which our projections account for, can be a third factor, but they have not played a major role in the tournament so far this year.)

In general – and with my apologies to those of you who had Gonzaga in your bracket – the teams that were well regarded by our model before the tournament started have survived intact, if sometimes bruised. The 11 teams that the model initially assigned the best chances of winning the tournament were Louisville (a 23.8 percent chance), Indiana (18.4 percent), Florida (13.2 percent), Kansas (7.9 percent), Duke (6.0 percent), Gonzaga (5.6 percent), Ohio State (5.4 percent), Michigan (2.5 percent), Michigan State (2.3 percent), Miami (1.8 percent) and Syracuse (1.8 percent). Only Gonzaga has lost among that group. (Georgetown — 0.9 percent — and New Mexico — 0.7 percent — also endured major upsets based on their seeding lines, but they were teams that statistical methods weren’t sold on to begin with.) With some important exceptions, more teams are now facing their nightmare draws than their dream ones. What follows are quick profiles of the 16 remaining teams and how their chances have changed from our initial estimates.

Louisville (up to 32.4 percent from 23.8 percent) Three of the four No. 1 seeds survived into the tournament’s second week, but only Louisville looked dominant in doing so, winning its first two games by a combined 57 points. Louisville also caught a break with its Round of 16 opponent, Oregon — which may well have been underseeded as a No. 12 but which nevertheless offers a much more favorable matchup than No. 4-seeded St. Louis might have (especially in a game played in Indianapolis).

Louisville wouldn’t be so fortunate in its potential Round of 8 matchup: either Duke or Michigan State will be very tough. But should Louisville win that game, it will play the champion from the depleted West bracket in the national semifinal. (Not much of a bonus if that opponent is Ohio State, but Louisville has two chances for the Buckeyes to lose.) Between their strong play so far and the favorable contingencies in their draw, the Cardinals have emerged as a true tournament favorite.

Indiana (down to 10.9 percent from 18.4 percent) This is a big decline for Indiana — the model estimates that its chances of winning the national title have dropped by 60 percent. One factor is Indiana’s close call on Sunday against Temple, a team that the computer ratings did not regard as very strong. But perhaps more important, the rest of the top seeds in the East Region have won out. The immediate problem is Indiana’s matchup Thursday against Syracuse, a team that our formula liked to begin with and which has played very well so far. That game will take place at the Verizon Center in Washington, an arena that Syracuse will find familiar from its Big East matchups against rival Georgetown. Indiana’s Round of 8 matchup might actually be easier by comparison, especially if Marquette upsets Miami.

Florida (up to 21.3 percent from 13.2 percent) The Gators are this year’s flash point in the debate between stat geeks and traditionalists. The traditionalists look at Florida’s 0-6 record in single-digit games and see it as an inability to close out in the clutch. “Statheads” like me attribute it to bad luck instead, and conclude that Florida is underrated as a result.

So far, the theories about how Florida might perform in close games haven’t been tested, since it won its first two games in dominant fashion. (The FiveThirtyEight model, of course, regards the blowout wins as yet more evidence that Florida is a very strong team.)

Florida will play Florida Gulf Coast in Arlington, Tex., on Friday. We’ll contemplate Florida Gulf Coast’s chances later on, but even if one takes an optimistic view toward the team, that counts as an awfully favorable matchup for Florida relative to the alternatives – and another reason that Florida has leapfrogged Indiana in our rankings.

Kansas (down to 4.5 percent from 7.9 percent) The decline in Kansas’ winning odds might seem a bit punitive, but the Jayhawks played three underwhelming halves of basketball before finally turning it on against North Carolina late on Sunday. Kansas will have much less margin for error against No. 4 seed Michigan, its opponent on Friday, and then in a potential matchup against Florida over the weekend, two teams that are well regarded by the model. (Our model establishes Kansas as only a 55 percent favorite against Michigan, and has the team as a slight underdog to Florida.) In fact, it didn’t help Kansas that the No. 2 seed, Georgetown, was eliminated from its region, since that only helped to clear a path for Florida.

Duke (unchanged at 6.0 percent) This is the rare case in which a team’s path might get easier the further it goes in the tournament. First, the good news for Duke fans: The Blue Devils should be plenty dangerous if they reach the Final Four in Atlanta, with the model giving them one-in-three odds of winning the tournament if they do. The problem is that their next two potential opponents, Michigan State and Louisville, have played very well, and both would have something of a “home region” advantage with the games to be played in Indianapolis.

Ohio State (up to 6.8 percent from 5.4 percent) The model sees one big negative for Ohio State: its close and somewhat fortunate win against Iowa State on Sunday. However, this is outweighed by the improvement in its draw with No. 1-seeded Gonzaga having been eliminated from the West Region.

The Buckeyes will also play No. 6 seed Arizona rather than No. 3 New Mexico on Thursday, but that isn’t as much of a blessing: Arizona may well have been the better team, and the game will be played in Los Angeles. Ohio State hasn’t traveled farther west than Lincoln, Neb., to play a game all season, so this could be a de facto road game for Aaron Craft and his teammates.

Michigan (up to 3.8 percent from 2.5 percent) Michigan could easily enough have been a No. 1 seed had it played better down the stretch, and it was probably underseeded as a No. 4 even with the losses that it took. In general, however, we’ve found that late-season performance doesn’t tell you that much more than early-season performance when it comes to tournament play – and Michigan’s slump has not extended into the postseason. It was a break for the Wolverines to play in Auburn Hills, Mich., but their domination of a tough Virginia Commonwealth team on Saturday was nevertheless impressive, and they should be thought of as the equivalent of a strong No. 2 seed right now.

Michigan State (up to 3.5 percent from 2.3 percent) Michigan and Michigan State have both had some strong eras as basketball programs, but this is the first time that the teams have appeared in the Round of 16 together. Their situations are quite parallel now in that both are very strong teams that face very difficult draws in their next two games. Michigan State will also have to monitor the status of point guard Keith Appling, who left Saturday’s game against Memphis after aggravating a shoulder injury.

Miami (up to 2.4 percent from 1.8 percent) Miami is something of the opposite case from its intrastate rival Florida; statistically based rankings liked the Hurricanes much less than human polls did. Their four-point win against Illinois on Sunday represents something of an equivocal data point: does Miami deserve praise for toughing out the win, or suspicion for struggling at times against a No. 7 seed and benefiting from some favorable officiating decisions? It should be favored against Marquette on Thursday, but either Indiana or Syracuse would put the Hurricanes to the test.

Syracuse (up to 4.8 percent from 1.8 percent) Syracuse’s 47-point win against Montana on Thursday was the largest ever by a team not seeded No. 1 or No. 2 (beating, as it happened, a record that Virginia Commonwealth had set less than an hour earlier). That is, of course, an impressive accomplishment to a model like ours that weighs margin of victory, so Syracuse’s chances of winning the tournament have more than doubled as a result. As with Michigan, this is a case in which late-season performance did not prove all that much: if the Orange are back in the early-season form that saw them start the season 18-1 and beat Louisville, they will make a very tough opponent for Indiana.

Marquette (down to 0.5 percent from 0.6 percent). Marquette’s draw against Davidson and Butler was tougher than it might look from the seeding, but it won the games by just three points combined — and the Golden Eagles are in the East Region, where the other top seeds have survived. Thus, Marquette’s chances of winning the tournament have not improved at all according to the model – instead, the team has been jumped by several others that began with worse seeds.

Arizona (up to 1.8 percent from 0.6 percent) One of those teams is Arizona, which the computer rankings now regard as tantamount to a No. 4 seed (rather than its nominal No. 6) after easy victories against Belmont and Harvard. Ohio State, Arizona’s opponent on Thursday, is a huge obstacle, but the game will be played in Los Angeles, and if the Wildcats win it, they should be favored against either Wichita State or La Salle in the regional final.

Wichita State (up to 1.2 percent from 0.1 percent) Wichita State has had as favorable a tournament as any team in the country so far. Its win against No. 1-seeded Gonzaga on Saturday got lots of attention, but the team also crushed No. 8-seeded Pittsburgh in its first game, a team that the computer rankings regarded highly. As their reward, the Shockers will face an overachieving La Salle team in the Round of 16. Their next game, against Ohio State or Arizona, would be much tougher, but Wichita State’s chances of reaching the Final Four are up to 24 percent — improved from just 1.3 percent before the tournament began.

Oregon (up to 0.06 percent from 0.01 percent) Those who complained that Oregon was underseeded have plenty of evidence in the form of wins against No. 5-seeded Oklahoma State and No. 4-seeded St. Louis. However, the Ducks’ punishment from the bracket makers is not over, as they’ll have to travel across the country to face the No. 1 overall seed, Louisville; the model gives them only about a 5 percent chance of winning that game.

La Salle (up to 0.10 percent from 0.01 percent) It’s tempting to draw parallels between La Salle and Virginia Commonwealth in 2011. Like the Commodores that year, this year’s Explorers were a controversial choice for the bracket that soon quieted all the talk by starting to win every game that it played.

But how likely is it that La Salle can replicate Virginia Commonwealth’s streak by winning five straight games (including a play-in game) en route to a Final Four appearance? The model gives the team only about a 5 percent chance, largely because Ohio State looms over the Explorers should they make it past Wichita State.

Florida Gulf Coast (up to 0.02 percent from 0.001 percent) It took Florida Gulf Coast about 48 hours to go from the butt of jokes to one of the most memorable tournament stories in history. But just how unlikely was it for the team to have reached the Round of 16?

Our model gave Florida Gulf Coast roughly a 3.3 percent chance of reaching the Round of 16 before the tournament began. That’s a low figure, but higher than that of the other three No. 15 seeds, whose chances ranged between 1.1 percent (Albany) and 2.6 percent (Pacific). It’s also slightly higher than that of La Salle, which was given a 2.7 percent chance, partly because it had to win three rather than two games to get there.

This is not meant to cast aspersions on Florida Gulf Coast. On the contrary, it reflects the fact that it was reasonably dangerous for a No. 15 seed; Ken Pomeroy’s ratings regard the team as having played the 14th-toughest nonconference schedule in the country, and it came up with a big win in one of those games, against Miami. (The team also lost games to the likes of Maine, Lipscomb and East Tennessee State; nobody should be suggesting that it ought to have been a No. 1 seed.) It also helped Florida Gulf Coast to have a relatively favorable draw, facing Georgetown, which our model regarded as the worst of the No. 2 seeds this year.

Even though these were unusually good circumstances for a No. 15 seed, it is probably somewhat unlucky that no No. 15 seed has made it to the Round of 16 before. If you assume that a typical No. 15 seed has a 2 percent chance of making it to the Round of 16, the chances that not one of them would do so before this year (there had been 112 previous opportunities since the tournament expanded to 64 teams in 1985) were only about 10 percent.

By the same logic, No. 16 seeds as a group are probably somewhat unlucky to have never won a tournament game. Our model typically gives a No. 16 seed something like a 2 percent chance of beating a No. 1 — about the same as a No. 15 seed’s winning two games and reaching the Round of 16. Any given No. 16 seed would have to be incredibly lucky to pull it off. But there have been 116 matchups between No. 1 and No. 16 seeds in the tournament’s history; with so many chances, the probability is that one or more of those teams would have punched their lottery ticket by now.

The point is simply that the tournament offers lots and lots of opportunities for highly improbable things to happen, so some of them happen in almost every tournament.

Suppose, however, that we limit our consideration of unlikely events to a team’s advancing to a certain stage of the tournament despite facing the longest odds initially. By this definition, the most unlikely event in the tournament’s history was perhaps Virginia Commonwealth’s run to the Final Four in 2011; in an article in 2011, I estimated that the odds of that were about 820-to-1 against.

To beat Virginia Commonwealth’s mark, Florida Gulf Coast will have to reach the Final Four itself; our model put the odds of this as about 2000-to-1 against before the tournament began.

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The odds that Florida Gulf Coast will reach the Final Four are much shorter now that the team has won its first two games, of course, but the model still puts the team at about 130-to-1 against, partly because it now has a very tough draw and will have to face Florida, and then either Kansas or Michigan.

As a mathematical aside, you may see even longer odds against Florida Gulf Coast quoted by other statistical systems. The difference is that the FiveThirtyEight model does not assume that the odds of winning any one tournament game are independent of the next one, as the other systems largely do. Instead, the assumption built into the FiveThirtyEight model is that once a team has overperformed its initial rating, its chances of continuing to do so have improved.

The runs made by teams like Virginia Commonwealth and Butler in the past are unlikely by any definition, but sometimes teams really are much stronger than their advance billing. That is most likely the case for Florida Gulf Coast, which has not only won two games but has also looked outstanding in doing so. It will now have to continue its magic against some of the best teams in the tournament.

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This is an archive of posts from FiveThirtyEight, a blog founded by Nate Silver in 2008 and devoted to rigorous, data-driven analysis of politics, polling, public affairs, sports, economics, science and culture, from August 2010 through July 2013.